This other equation is linked with equation (REF )
through the non-autonomous Möbius transformation [1]}
\(y_{n, m} = \big ( F^{(+)}_{n}F^{(+)}_{m}+F^{(-)}_{n}F^{(-)}_{m}\big )v_{n, m}+\frac{F^{(-)}_{n}F^{(+)}_{m}+F^{(+)}_{n}F^{(-)}_{m}}{v_{n, m}}. \) 

